6. Empirical findings and analysis
6.1 Performance evaluation
To evaluate the performance of Danish mutual funds, two models was estimated for each fund. The Jensen model which test for stock-picking skills of the fund manager, and the Treynor and Mazuy model, which besides stock-picking skills also test for the fund managers ability to time the market.
6.1.1 Jensen’s Alpha
The null hypothesis in the Jensen’s alpha model states that the alpha 𝛼 is equal to zero, while the alternative states that the 𝑎 is significant different from zero.
𝐻0: 𝛼 = 0 𝐻1: 𝛼 ≠ 0
A failure to reject the null hypothesis indicates that all the return of the fund can be explained by the return of the market. A rejection of the null hypothesis imply that the fund has generated return either lower or higher than what can be explained by the market portfolio. A statistically significant negative alpha imply that the fund has generated returns lower than the selected benchmark, and that the fund would have performed better if just using a naïve buy-the-market and hold strategy. A significant positive alpha imply that the fund managers attempt in selecting stocks that generate returns higher than one would expect by their given level of risk, has been successful.
6.1.2 Treynor and Mazuy market timing model
The Treynor and Mazuy market timing model, includes both and alpha and a gamma. The alpha of the model will, just like the Jensen model, capture the selection skills of the fund manager, while the gamma capture the fund managers ability to adjust the portfolio 𝛽 according to fluctuations in the market. A significant positive gamma implies that the fund manager has been successful in timing the market, while a significant negative gamma means that the manager has mistimed the adjustment of the beta according to the market.
The hypothesis of the Treynor and Mazuy market timing model is:
𝐻0: 𝛼 = 0 𝐻1: 𝛼 ≠ 0
𝐻0: 𝛾 = 0 𝐻1: 𝛾 ≠ 0
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6.1.3 Gross Returns
The estimates for the models using gross returns is presented in table 6.1 and 6.2. The results are presented for each category, and for the total sample. The coefficients for the models are shown as the average for each group, along with the Newey-West robust standard error in parentheses below.
6.1.3.1 Jensen’s Alpha - Gross return
Table 6.1- Jensen's Alpha - monthly gross returns
Alpha
N 𝑅𝑎𝑑𝑗2 Beta Alpha No. Signif Low High (Neg)/Pos
Denmark 20 0.88538 1.01100 0.000612 (0)/0 -0.001272 0.003267 (5)/15
(0.0307) (0.0014)
Europe 16 0.82467 1.00494 0.000091 (0)/0 -0.002498 0.001936 (9)/7
(0.0424) (0.0016)
Global 30 0.77152 1.01777 0.000222 (0)/0 -0.001678 0.002499 (15)/15
(0.0511) (0.0017)
Total 66 0.81891 1.01261 0.000309 (0)/0 -0.002498 0.003267 (29)/37
(0.0428) (0.0016)
The table shows the average coefficients and the Newey-West robust standard errors in parentheses below.
Column No. Signif show the number of funds with a significant (negative)/positive alpha on a 5 percent significance level. The last three columns show the lowest and highest alpha in each group, along with total number of funds with a (negative)/positive alpha.
The adjusted 𝑅2 of each group falls between 77% and 89% and indicates the percentage of the return which is explained by the model. This is a relatively high power of explanations, though not as high as found by Christensen (2005, 2013).
The average beta for each group and for the total sample is all above, but very close to one, indicating that the net returns of the funds are slightly more volatile than their respective benchmark. The average alpha for all groups and for the total sample is positive. The group investing in Denmark, has an average alpha of 0.06%, which corresponds to a yearly return of 0.73% above their benchmark, the highest among the three groups. Three out of every four of the funds in the group investing in Denmark, have a positive alpha, while less than half of the funds investing in Europe generated positive alphas. For the group with a global investment focus, half of the funds had positive alphas in the period. In total 37 (56%) out of the full sample of 66 funds have a positive alpha, which indicates that the mutual funds on average can generate returns higher than their benchmark, when expenses are not accounted for. Though this is only indications, as none of the mutual fund’s actual generated an alpha significantly different from zero at the 5-percent significance level.
Looking at the fund individually there is some distance between highest and lowest average alpha. Lowest monthly alpha is -0.25% and found at the group investing in Europe. This indicates that the fund generates a
44 risk adjusted yearly return which is 3% lower than the corresponding benchmark. The highest alpha is found at the group Denmark, is 0.33%, and corresponds to the fund outperforming their benchmark with almost 4% per year. Though these two values can be seen as rather extreme, the p-value of the alphas is 0.45 and 0.17 respectively and can therefore not be concluded as significant. This is due to large standard errors of the coefficient, caused by high variance of the return data.
The average alpha of the sample is 0.03% which corresponds to the funds before expenses, generate a yearly return 0.37% above their benchmark. With the average yearly expense ratio being 1.39% this is hardly enough to cover the expenses of the active funds. The number of funds with negative alphas is therefore expected to increase when examining performance net of return.
6.1.3.2 Treynor and Mazuy - Gross return
Table - 6.2 Treynor and Mazuy market timing model - monthly gross returns
Alpha Gamma
N 𝑅𝑎𝑑𝑗2 Beta Alpha
No.
Signif Low High
(Neg)/
Pos Gamma
No.
Signif
(Neg)/
Pos Denmark 20 0.887 1.01509 0.00044 (0)/1 -0.0016 0.0070 (11)/9 0.03273 (2)/5 (7)/13
(0.0320) (0.0016) (0.3511)
Europe 16 0.827 0.99093 0.00124 (0)/1 -0.0042 0.0033 (2)/14 -0.69958 (5)/0 (12)/4
(0.0436) (0.0019) (0.6998)
Global 30 0.774 1.01275 0.00056 (0)/1 -0.0044 0.0038 (9)/21 -0.19381 (6)/1 (19)/11
(0.0523) (0.0020) (0.8984)
Total 66 0.821 1.00817 0.00068 (0)/3 -0.0044 0.0070 (22)/44 -0.24777 (13)/6 (38)/28
(0.0442) (0.0018) (0.6844)
The table shows the average coefficients and the Newey-West robust standard errors in parentheses below.
Column No. Signif show the number of funds with a significant (negative)/positive alpha or gamma on a 5 percent significance level. The column (Neg)/Pos show the total number of funds with a (negative)/positive alpha and gamma. The columns Low and High, show the lowest and highest alpha in each group.
The explanatory power 𝑅𝑎𝑑𝑗2 , have no noteworthy changes compared to the Jensen model, so the quadratic term included in the Treynor and Mazuy market timing model, have not helped to improve the explanation of the mutual funds return. But it has helped in explaining the differences in the return generated from the fund managers ability to select stocks, and her ability to exploit the fluctuations in the market. The average alpha for the total sample, and for the groups individually is still positive. When comparing the results with the Jensen model, the average alpha has now decreased for the group Denmark while it has increased for the groups Europe and Global. Furthermore, there is now three of the funds which have a significant positive alpha, one in each group. This imply that these three funds have poor market timing, which reduces the alpha and make it non-significant under the Jensen model.
45 The reduction in the average alpha of the funds investing in Denmark, suggest that the abnormal returns is not only generated through stock-picking, but also through successive market timing, shown by the positive average gamma of the group. The opposite is the case for the other two groups, as the average alpha has increased. This imply that the selection of stocks actually has been more successful, than suggested by the Jensen model, but poor market timing, has reduced the overall return of the funds, which also can also be deducted from the average negative gamma by the two groups.
The group Denmark has an average positive gamma of 0.0327, and 13(65%) of the funds have a positive gamma, of which five is significant at the 5-percent level. Two of the funds in the group generated a significant negative gamma. Of the 16 funds, investing in European stocks 12(75%) have a negative gamma, of which five is significant. Only four funds have a positive gamma in this group, and none is significant, and with an average gamma of -0.70 this imply poor market timing for this group. For the funds with a global investment focus, 19 (64%) have negative gamma, of which 6 is significantly negative. For the whole sample 13(20%) have significantly negative gamma, and with an average gamma of -0.248, this tells that the funds on average is not capable of timing the market.
6.1.3.3 Intermediate conclusion - Gross return
None of the funds generates significant alphas when using the Jensen model and only three have significant positive alphas when using the market timing model. As these models is calculated before accounting for expenses, one would expect more funds to outperform the market. Though these result is much in line with the findings of Christens (2005). The overall assessment of the funds is that they do not possess the ability to time the market. Though looking at the three groups it is noteworthy that it is primarily funds with a European or Global investment focus which have significant negative gamma, while 25% of the funds investing in Denmark has positive significant gammas. This can indicate that it is easier for fund managers to time the Danish market compared to the European or global stock market. One reason could be that the OMX CPH CAP INDEX includes fewer shares, and the C25 companies make up the main part of the index. Fewer stocks make single company events more likely to influence the return of the index, so that correct stock-picking, could also result in correct market timing.
6.1.4 Net Returns
6.1.4.1 Jensen’s Alpha - Net return
When calculating the Jensen model using net return instead, the impact of the costs is clearly shown on the performance. The average alpha has now turned negative for all groups, and only 16(24%) funds out of the total sample now has a positive alpha, with all of them being insignificant. The only significant alpha is negative and found at the group Denmark. This fund has from 2006 to 2018 generated an average monthly
46 return being -0.23% lower than their corresponding benchmark. This corresponds to an underperformance of -2.8% per year over a 12-year period. The highest alpha is also found at the group Denmark and is 0.19%.
Though the majority of the funds have a negative alpha, only one fund is tested to significant different from zero. Therefore, the overall assessment of the fund performance using net returns, is that they perform neutrally.
Table 6.3 - Jensen's Alpha - monthly net returns
Alpha
N 𝑅𝑎𝑑𝑗2 Beta Alpha No. Signif Low High (Neg)/Pos
Denmark 20 0.88538 1.01099 -0.000483 (1)/0 -0.002323 0.001995 (14)/6
(0.0307) (0.0014)
Europe 16 0.82457 1.00471 -0.001066 (0)/0 -0.003345 0.000628 (12)/4
(0.0424) (0.0016)
Global 30 0.77141 1.01759 -0.000947 (0)/0 -0.002535 0.001539 (24)/6
(0.0511) (0.0017)
Total 66 0.81883 1.01247 -0.000835 (1)/0 -0.003345 0.001995 (50)/16
(0.0428) (0.0016)
The table shows the average coefficients and the Newey-West robust standard errors in parentheses below.
Column No. Signif show the number of funds with a significant (negative)/positive alpha on a 5 percent significance level. The last three columns show the lowest and highest alpha in each group, along with total number of funds with a (negative)/positive alpha.
6.1.4.2 Treynor and Mazuy - Net return
The comparison of the Jensen model with the Market timing model using net returns, is very similar to the comparison using gross return. There is still an increase in the average alpha for the total sample, and for the groups with a European and global investment focus. The Average alpha for the group Europe has actually turned positive now but is extremely close to zero. The increase in alpha suggests poor market timing among fund managers in these two groups, which is additional supported by the average negative gamma and the number of significant negative gammas in the two groups. In the group investing in Denmark, 13(65%) had positive gamma, of which five funds had a significant positive gamma.
Table 6.4 - Treynor and Mazuy market timing model - monthly net returns
Alpha Gamma
N 𝑅𝑎𝑑𝑗2 Beta Alpha
No.
Signif Low High
(Neg)/
Pos Gamma
No.
Signif
(Neg)/
Pos Denmark 20 0.8868 1.01514 -0.00066 (1)/1 -0.00238 0.00572 (16)/4 0.03421 (2)/5 (7)/13
(0.0320) (0.0016) (0.3511)
Europe 16 0.8267 0.99076 0.00007 (0)/0 -0.00510 0.00201 (6)/10 -0.69634 (5)/0 (12)/4
(0.0436) (0.0019) (0.6999)
Global 30 0.7741 1.01262 -0.00062 (0)/0 -0.00555 0.00258 (18)/12 -0.18839 (6)/1 (19)/11
(0.0523) (0.0020) (0.8985)
Total 66 0.8210 1.00808 -0.00046 (1)/1 -0.00555 0.00572 (40)/26 -0.24407 (13)/6 (38)/28
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(0.0442) (0.0018) (0.6845)
6.1.4.3 Intermediate conclusion - Net returns
Results from the two models using net returns, supports the conclusion that the Danish mutual fund managers do not possess stock picking skills. Net of expenses all but one fund performed neutral, and the last fund performed significantly worse than market. When it comes to market timing, the conclusion is the same as for gross returns. Both gross and net of returns mutual funds investing in the European and global market have poor market timing, while some of those funds investing in Denmark seems to be able to time the market. These results are much in line with the findings made by Christensen (2005,2013). He found that almost half of the fund had significant negative alpha, though his sample period went from 2001 to 2010 including both the tech bubble, and the financial crisis, which could have an effect on his results.
Furthermore, did he found that 64% of the funds with Danish investment focus had market timing, while this was only 6% for the rest of the examined funds. This add to the assumption that Danish fund managers are better to time fluctuations at the Danish market, though Christensen does not comment on this in his paper.
6.1.5 Performance over a three-year period
To fully assess the performance of the Danish mutual funds, the Jensen model was also calculated using a three-year time period, and for a single year. This was done to see if the funds performed differently over shorter periods, which would lead to a better evaluation of their overall performance.
Table 6.5 - Jensen alpha using prior 36 months of gross return
2018-2016
2017-2015
2016-2014
2015-2013
2014-2012
2013-2011
2012-2010
2011-2009
2010-2008
2009-2007
2008-2006
Total Unique Funds Denmark (2)/0 (0)/1 (0)/4 (0)/4 (0)/2 (0)/0 (0)/0 (0)/0 (0)/1 (0)/0 (0)/0 (2)/12 (2)/6 Europe (1)/0 (0)/0 (0)/1 (0)/1 (0)/1 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (1)/3 (1)/2 Global (3)/0 (0)/0 (0)/0 (0)/1 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (3)/1 (3)/1 Total (6)/0 (0)/1 (0)/5 (0)/6 (0)/3 (0)/0 (0)/0 (0)/0 (0)/1 (0)/0 (0)/0 (6)/16 (6)/9
N 66 66 64 63 56 53 50 49 48 38 36 589
Number of funds with a significant alpha in each time period. Last column shoes number of unique funds with significant alphas over the time period.
Using only three years of data instead of the full period, several more funds now generates significant alphas.
A total of nine different funds has at least on time during these subperiods, generated a positive alpha. Some of the funds have generated a significant positive alpha in several periods, most of them is found in the group investing in Denmark. One fund in this group have even delivered significant positive alpha in the four consecutive periods and have significantly outperform the market in the years between 2012 to 2017. The
48 other significant positive alpha is generated in this period as well. Six funds have generated a significant negative alpha, all of them in the period from 2016-2018.
Table 6.6 - Jensen alpha using prior 36 months of net return
2018-2016
2017-2015
2016-2014
2015-2013
2014-2012
2013-2011
2012-2010
2011-2009
2010-2008
2009-2007
2008-2006
Total Unique Funds Denmark (5)/0 (0)/0 (0)/1 (0)/4 (0)/1 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (5)/6 (5)/4 Europe (2)/0 (0)/0 (0)/0 (0)/0 (0)/0 (1)/0 (0)/0 (1)/0 (0)/0 (0)/0 (0)/0 (4)/0 (3)/0 Global (6)/0 (1)/0 (1)/0 (0)/1 (0)/0 (1)/0 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (9)/1 (8)/1 Total (13)/0 (1)/0 (1)/1 (0)/5 (0)/1 (2)/0 (0)/0 (1)/0 (0)/0 (0)/0 (0)/0 (18)/7 (16)/5
N 66 66 64 63 56 53 50 49 48 38 36 589
Number of funds with a significant alpha in each time period. Last column shoes number of unique funds with significant alphas over the time period.
When accounting for expenses the number of funds which deliver a significant negative alpha is now increased to 16, with 13 of these found in the period 2016-2018. This is 20% of the funds that significantly underperform their benchmark at least on time in over a three-year period. Five funds were able to generate a positive alpha, even when accounting for expenses. Of these, four of them invested in the Danish market.
6.1.6 Performance over 12 months
Reducing the evaluation period to only 12 months, can help to point out years with have effect on the overall performance of the funds. The use of only 12 datapoints in the regression is in many cases also increasing the standard errors, which decreases the likelihood of a significant result.
Before expenses 16 funds have a significant positive alpha and 14 have a significant negative alpha. This suggest very little persistence among the funds, as the significant alphas are spread out across different funds. Only two funds have generated a significant alpha in more than one year, and only three funds have performed significant worse more than one year. The positive alphas are concentrated at the years, 2014, 2015 and 2017, with 15 of the significant alphas gross of expenses observed here. This is rather telling that in a 13-year period, even before expenses there is only three years where funds are able to significantly outperform their benchmark.
Table 6.7 - Jensen alpha using prior 12 months of gross return
2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 Total Unique Denmark (3)/0 (0)/0 (0)/0 (0)/4 (0)/3 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (1)/0 (0)/0 (4)/7 (4)/5 Europe (1)/0 (0)/1 (0)/0 (0)/3 (0)/1 (0)/0 (0)/0 (1)/0 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (2)/5 (2)/5 Global (2)/0 (0)/3 (6)/0 (0)/2 (0)/1 (0)/0 (0)/0 (1)/0 (0)/0 (0)/0 (0)/0 (1)/1 (0)/0 (10)/7 (8)/6 Total (6)/0 (0)/4 (6)/0 (0)/9 (0)/5 (0)/0 (0)/0 (2)/0 (0)/0 (0)/0 (0)/0 (2)/1 (0)/0 (16)/19 (14)/16
49
N 66 66 66 66 64 63 56 53 50 49 48 38 36 721
Net of expenses only seven funds were able to generate a significant positive alpha and outperform their benchmark, while 21 funds significantly underperformed compared to their benchmark. Out of the 24 observed negative alphas 15 are found in the two years 2016 and 2018. With so few funds that over- or underperform more than one year, it seems that this happens more by coincidence than an effect of stock-picking skills. The overall assessment of the funds’ performance will therefore be addressed as neutral.
Table 6.8 - Jensen alpha using prior 12 months of net return
2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 Total Unique Denmark (5)/0 (1)/0 (0)/0 (0)/1 (0)/1 (1)/0 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (1)/0 (1)/0 (9)/2 (8)/2 Europe (1)/0 (1)/0 (1)/0 (0)/2 (0)/0 (0)/0 (0)/0 (1)/0 (0)/0 (0)/0 (0)/0 (0)/0 (0)/0 (4)/2 (4)/2 Global (2)/0 (0)/2 (6)/0 (0)/0 (0)/0 (0)/0 (0)/0 (2)/0 (0)/0 (0)/0 (0)/0 (1)/1 (0)/0 (11)/3 (9)/3 Total (8)/0 (2)/2 (7)/0 (0)/3 (0)/1 (1)/0 (0)/0 (3)/0 (0)/0 (0)/0 (0)/0 (2)/1 (1)/0 (24)/7 (21)/7
N 66 66 66 66 64 63 56 53 50 49 48 38 36 721
6.1.7 Intermediate conclusion - Performance evaluation
Using 12 and 36 months of return data to evaluate the performance, did not deliver much support for the existence of stock-picking skills among the fund managers. Before accounting for expenses there is not much difference between the number of funds which significantly outperform their benchmark, compared to the number of funds which significantly underperform, and after accounting for expenses three times as many funds had significant negative alphas as positive. Though several funds generated significant alphas in individual years, very few funds did so in several years. Those who did outperform their benchmarks, were often found among those funds investing in Denmark, and one fund in this group was able to outperform the market in four consecutive time periods of three years. When looking at the funds as a total group, very little persistence exists among the funds. Many of the funds over- or underperform the benchmark in the same years. This can happen if the funds have a portfolio with beta which always is more than one. Then the fund will overperform when market goes up and underperform when the general market goes down. When the funds over- or underperform according to their benchmark, it therefore seems more as isolated incidents caused by the fund’s choice of beta being more than one, rather than the effect of stock-picking skills or lack of by the manager.